本研究提出適用於乳化液在冷軋塑液動潤滑模型，以牛頓-瑞福遜法求解油水兩相之等效雷諾方程式及薄板塑性變形方程式。在數值模擬中，影響冷軋塑液動潤滑模型收斂最主要的二個因素，為進口端油膜厚度以及薄板進口區速度，而進口端油膜厚度可由Willson & Wallowit公式[5]估算當作猜值。而本文探討初始油相比、滾輪速度、縮減比、前向張力、後向張力、黏度壓力係數及表面張力群對於乳化液潤滑特性之影響。
結果發現提高滾輪速度會增加油膜厚度，但對於油膜壓力、負荷及轉矩則影響不大。此外，油膜厚度會隨著黏度壓力係數增加而增加，當黏度壓力係數太低時，則需藉由增加前向張應力產生液動潤滑。在進口區咬角前，因為乳化液油水二相黏度的差異，金屬對於油相有較高的親和力，水相因而被排斥在外，而產生油池，使得初始油相比較低的乳化液，在塑性區具有較高的油相比進而形成較厚的油膜厚度。而表面張力群為形成油池最主要的原因，滾輪速度及縮減比則能增加咬角前油相比。

In this study, a model suitable for the plasto-hydrodynamic lubrication of cold rolling with the oil-in-water emulsions has been developed. The coupled modified Reynolds and von Karman equations are solved by the Newton-Raphson method. In the numerical simulation, the main factors of influencing the numerical convergence are the initial guess for the inlet film thickness and the inlet speed of strip. The inlet film thickness can be estimated by the Wilson and Walowit formula [5]. The effects of oil volume fraction, surface speed of roller, reduction ratio, forward tension, backward tension, pressure viscosity coefficient, and surface tension group on the lubricating properties of cold rolling are investigated.
Results show that the film thickness increases with increasing surface speed of roller, but its effects on the film pressure, the roll force and the roll torque are not conspicuous. In addition, the film thickness increases as the pressure viscosity coefficient increases. In the condition of the very low pressure viscosity coefficient, hydrodynamic lubrication of cold rolling works by enhancing the forward tension. Ahead of the roll bite, the metal surface has a higher affinity to the oil phase so that water is excluded and the oil pooling is formed because of the difference in the viscosity of the two components of the emulsion. Hence, in the condition of the lower initial oil volume fraction, the thicker film thickness is formed by the higher oil volume fraction in the work zone due to the oil pooling. The oil pooling is mainly influenced by the surface tension group. The surface speed of roller and the reduction ratio could enhance the oil volume fraction ahead of the roll bite.

總　目　錄

頁次
總目錄 i
圖目錄 v
表目錄 ix
符號說明 x
中文摘要 xiii
英文摘要 xiv

第一章　緒論 1
1.1　研究動機 1
1.2 乳化液概述 1
1.3 文獻回顧 2
1.4　本文重點 5
1.5 論文架構 5
第二章　理論分析 7
2.1 前言 7
2.2 基本假設 8
2.3　無因次化 10
2.4 黏度方程式 10
2.5 進口區分析 11
2.5.1 油膜厚度的幾何分析 11
2.5.2 純油雷諾方程式 12
2.5.3 乳化液雷諾方程式 12
2.5.4 剪應力方程式 13
2.5.5 邊界條件 14
2.6 塑性區分析 14
2.6.1　薄板及油膜厚度的幾何分析 14
2.6.2　純油雷諾方程式 15
2.6.3 乳化液雷諾方程式 16
2.6.4 剪應力方程式 17
2.6.5 邊界條件 17
2.6.6 薄板塑性變形方程式 18
2.7 出口區分析 18
2.7.1 油膜厚度的幾何分析 18
2.7.2 純油雷諾方程式 19
2.7.3 乳化液雷諾方程式 19
2.7.4　剪應力方程式 20
2.7.5　邊界條件 21
2.8　進口及出口位置 21
2.8.1 進口位置 21
2.8.2 出口位置 22
2.9 其它相關參數方程式 22
2.9.1 滾輪負荷 22
2.9.2 滾輪轉矩 22
第三章　數值分析 23
3.1 純油 24
3.1.1　進口區 24
3.1.2 塑性區 25
3.1.3 出口區 28
3.2 乳化液 29
3.2.1 進口區 29
3.2.2 塑性區 33
3.2.3 出口區 39
第四章　結果與討論 41
4.1 純油 41
4.1.1 滾輪速度對於冷軋特性的影響 41
4.1.2 縮減比對於冷軋特性的影響 42
4.1.3　 前、後向張應力對於冷軋特性的影響 43
4.1.4 黏度壓力係數對於冷軋特性的影響 44
4.1.5 彈性變形對於冷軋特性的影響 44
4.1.6 簡易雷諾方程式對於冷軋特性的影響 45
4.2 乳化液 45
4.2.1　油相比對於冷軋特性的影響 45
4.2.2 滾輪速度對於冷軋特性的影響 46
4.2.3　縮減比對於冷軋特性的影響 47
4.2.4　前、後向張應力對於冷軋特性的影響 48
4.2.5 黏度壓力係數對於冷軋特性的影響 48
4.2.6 表面張力群對於冷軋特性的影響 49
第五章　結論與建議 50
5.1 結論 50
5.2 建議 52
參考文獻 97

1. H. S. Cheng, ”Plastohydrodynamic Lubrication”, Friction and Lubrication in Metal Processing, ASME Book, 1966, p.69.
2. D. S. Bedi and M. J. Hiller, “Hydrodynamic Model for Cold Rolling”, Proc. Inst. Mech. Engs.,1967-1968, p.153.
3. W. R. D. Wilson and S. M. Mahdavian, J. Lubr. Technol., 96 (4) (1974), p.572-578.
4. T. A. Dow, J. W. Kannel and S. S. Bupara, “A Hydrodynamic Lubrication Theory for Strip Rolling including Thermal Effects”, J. Lubr. Tech., ASME 1975, p.412.
5. W. R. D. Wilson and M. J. Walowit, ”An Isothermal Hydrodynamic Lubrication Theory for Strip Rolling with Front and Back Tension.”, in Tribology Convension, Int.Mech.Eng., London, 1971, p.164-172.
6. P. M. Lugt, A. W. Wemekamp, W. E. ten Napel, P. van Liempt and J. B. Otten, Wear, Volume 166, Issue 2, 1 July 1993, p.203-214.
7. A. Al-Sharif, K. Chamniprasart, K. R. Rajagopal and A. Z. Szeri, “Lubrication with Binary Mixtures : Liquid–LiquidEmulsion” ASME, J. Tribol., Vol. 115, 1993, p.46.
8. S. H. Wang, A. Al-Sharif, K. R. Rajagopal and A. Z. Szeri, “Lubrication with Binary Mixtures: Liquid-Liquid Emulsion in an
EHL Conjunction,” ASME, J. Tribol., Vol.115, 1993, p.515.
9. F. Dai and M. M. Khonsari, “A Theory of Hydrodynamic Lubrication Involving the Mixture of Two Fluids,” ASME, J. Appl. Mech., Vol.61, 1994, p.634.
10. S. Yan, and S. Kuroda, “Lubrication with Emulsion: First Report, the Extended Reynolds Equation,” Wear, Vol.206, 1997, p.230.
11. S. Yan, and S. Kuroda, “Lubrication with Emulsion II. The Viscosity Coefficients of Emulsions,” Wear, Vol.206, 1997, p.238-243
12. J. Benner, Hoeprich R. Sadeghi and C. Frank, “Lubricating Properties of Water in Oil Emulsions,” J. Tribol., Vol.128, 2006, p.296.
13. S. H. Wang, A. Z. Szeri and K. R. Rajagopal, “Lubrication With Emulsion in Cold Rolling”, Journal of Tribology, Transactions of the ASME, v 115,n 3, Jul,1993, p.523-531.
14. A. Z. Szeri and S. H. Wang, “An elasto-plasto -hydrodynamic model of strip rolling with oil/water emulsion lubricant,” Tribology, Vol.37, 2004, p.169.
15. P. B. Kosasih and A. K. Tieu, Tribology International, Volume 40, Issue 5, May 2007, p.709-716.
16. R. R. Hughes and E. R. Gilliland, “The Mechanics of Drops,” Chem. Eng. Progr.,Vol.48 , 1952, p.497.
17. J. C. Oldroyd, “The Elastic and Viscous Properties of Emulsions and Suspensions,” Proc. Roy. Soc., Series A218, 1953, p.122.
18. J. C. Oldroyd, “The Effect of Interfacial Stabilizing Films on the Elastic and Viscous Properties of Emulsions,” Proc. Roy. Soc., Series A232, 1955, p.567.
19. W. O. Williams and R. Sampaio, “On the Viscosities of Liquid Mixtures,” J. Appl. Math. Phy., Vol. 28, 1977, p.607.
20. C. Barus, “Isothermals, Isopiestics and Isometrics relative to viscosity”, Am. J. Sc., No.45, 1983, p.87.
21. C. J. A. Roelands, J. C. Vlugter and H. I. Watermann, “The Viscosity Temperature Pressure Relationship of Lubricating Oils and its Correlation with Chemical Constitution”, Journal of Basic Engineering, 1963, p.631.